A081172 -id:A081172 - cp's OEIS frontend

A255533 Indices of primes in the 9th-order Fibonacci number sequence, A251750.

10, 33, 43, 253, 1253, 2389

Offset: 1

Robert Price, Feb 24 2015

a(7) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251750.

a={0,0,0,1,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A255534 Indices of primes in the 9th-order Fibonacci number sequence, A251751.

Original entry on oeis.org

10, 12, 232, 502

Offset: 1

Robert Price, Feb 24 2015

a(5) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251751.

a={0,0,1,0,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Flatten[Position[LinearRecurrence[Table[1,{9}],{0,0,1,0,0,0,0,0,0},510], ?(PrimeQ[#]&)]]-1 (* _Harvey P. Dale, Feb 27 2016 *)

A255536 Indices of primes in the 9th-order Fibonacci number sequence, A251752.

Original entry on oeis.org

10, 11, 21, 29, 301, 57089

Offset: 1

Robert Price, Feb 24 2015

a(7) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251752.

a={0,1,0,0,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A268410 a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9.

Original entry on oeis.org

5, 7, 9, 21, 37, 67, 125, 229, 421, 775, 1425, 2621, 4821, 8867, 16309, 29997, 55173, 101479, 186649, 343301, 631429, 1161379, 2136109, 3928917, 7226405, 13291431, 24446753, 44964589, 82702773, 152114115, 279781477, 514598365, 946493957

Offset: 0

Ilya Gutkovskiy, Feb 04 2016

Tribonacci sequence beginning 5, 7, 9.

In general, the ordinary generating function for the recurrence relation b(n) = b(n-1) + b(n-2) + b(n-3), with n>2 and b(0)=k, b(1)=m, b(2)=q, is (k + (m-k)*x + (q-m-k)*x^2)/(1 - x - x^2 - x^3).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Tribonacci Number
Index entries for linear recurrences with constant coefficients, signature (1,1,1)

Cf. similar sequences with initial values (p,q,r): A000073 (0,0,1), A081172 (1,1,0), A001590 (0,1,0; also 1,2,3), A214899 (2,1,2), A001644 (3,1,3), A145027 (2,3,4), A000213 (1,1,1), A141036 (2,1,1), A141523 (3,1,1), A214727 (1,2,2), A214825 (1,3,3), A214826 (1,4,4), A214827 (1,5,5), A214828 (1,6,6), A214829 (1,7,7), A214830 (1,8,8), A214831 (1,9,9).

a:=[5,7,9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019

I:=[5,7,9]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2016

LinearRecurrence[{1, 1, 1}, {5, 7, 9}, 40]
RecurrenceTable[{a[0]==5, a[1]==7, a[2]==9, a[n]==a[n-1]+a[n-2]+a[n-3]}, a, {n, 40}]

my(x='x+O('x^40)); Vec((5+2*x-3*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019

((5+2*x-3*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019

G.f.: (5 + 2*x - 3*x^2)/(1 - x - x^2 - x^3).

a(n) = 3*K(n) - 4*T(n+1) + 8*T(n), where K(n) = A001644(n) and T(n) =A000073(n+1). - G. C. Greubel, Apr 23 2019

A280308 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=3, a(1)=4, a(2)=5.

Original entry on oeis.org

3, 4, 5, 12, 21, 38, 71, 130, 239, 440, 809, 1488, 2737, 5034, 9259, 17030, 31323, 57612, 105965, 194900, 358477, 659342, 1212719, 2230538, 4102599, 7545856, 13878993, 25527448, 46952297, 86358738, 158838483, 292149518, 537346739, 988334740, 1817830997, 3343512476, 6149678213, 11311021686, 20804212375

Offset: 0

Peter M. Chema, Dec 31 2016

Like other tribonacci sequences, the digital root is period length 39, and is as follows: (3, 4, 5, 3, 3, 2, 8, 4, 5, 8, 8, 3, 1, 3, 7, 2, 3, 3, 8, 5, 7, 2, 5, 5, 3, 4, 3, 1, 8, 3, 3, 5, 2, 1, 8, 2, 2, 3, 7).
Completes the set of tribonacci numbers with 3,4,5 as initial terms, the others being (3,5,4), (4,5,3), (4,3,5), (5,3,4), and (5,4,3). The sum of each of the digital root periods in the above set is 162, except (4,3,5), which sums to 180; the sum of the digital root period of A081172 is also 180.
Each digital root period for tribonacci sequences has triple patterns in cycles of 13, such as period (1,4,7) or digital root of 4^n.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).

Cf. A000073, A001590, A081172, A000213.

RecurrenceTable[{a[n] == a[n - 1] + a[n - 2] + a[n - 3], a[0] == 3, a[1] == 4, a[2] == 5}, a, {n, 38}] (* Michael De Vlieger, Dec 31 2016 *)
LinearRecurrence[{1, 1, 1}, {3, 4, 5}, 40] (* Vincenzo Librandi, Jan 01 2017 *)

G.f.: (3+x-2*x^2)/(1-x-x^2-x^3). - Vincenzo Librandi, Jan 01 2017

A230016 Indices of primes in the tribonacci-like sequence, A214825.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 10, 16, 17, 26, 32, 104, 109, 120, 133, 312, 546, 608, 2274, 2527, 2932, 4462, 4680, 6001, 7103, 17402, 17874, 20664, 26341, 27954, 32869, 36204, 41521, 49065, 64172, 66318, 196078

Offset: 1

Robert Price, Feb 22 2014

nonn

a(39) > 2*10^5.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Cf. A001590, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523,A214825, A235862.

a={1,3,3}; Print[1];Print[2]; For[n=3, n<=1000, n++, sum=Plus@@a; If[PrimeQ[sum], Print[n]]; a=RotateLeft[a]; a[[3]]=sum]

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A255533 Indices of primes in the 9th-order Fibonacci number sequence, A251750.

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A255534 Indices of primes in the 9th-order Fibonacci number sequence, A251751.

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A255536 Indices of primes in the 9th-order Fibonacci number sequence, A251752.

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A268410 a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9.

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A280308 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=3, a(1)=4, a(2)=5.

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A230016 Indices of primes in the tribonacci-like sequence, A214825.

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